Locking planes together and animating them separately with shape keys
You can (sortof) do it like this


set the pivot point for all the planes in the same exact point in 3d space.
this can be done in more then one way: you can join all them togheter (so that all meshes get one single pivot point) and then separate them back again, one by one (the pivot point of separated meshes remains untouched); another one would be manually "set origins" to one 3d point of your choice...
then select one plane as "base" and use "copy location" constraint on all the others, with the "base" one as target.







the constrained planes can't be moved anymore, if not moving the "base" one, which moves all the others too.
shape keys for each plane are still independent
for rotation/scale, just select all them, they will rotate/scale around the same pivot point for all so they will rotate/scale all together